The confinement of surface-state electrons by a complex supramolecular network is studied with low-temperature scanning tunneling microscopy and rationalized by electronic structure calculations using a boundary element method. We focus on the self-assembly of dicarbonitrile-sexiphenyl molecules on Ag(111) creating an open kagomé topology tessellating the surface into pores with different size and symmetry. This superlattice imposes a distinct surface electronic structure modulation, as observed by tunneling spectroscopy and thus acts as a dichotomous array of quantum corrals. The inhomogenous lateral electronic density distribution in the chiral cavities is reproduced by an effective pseudopotential model. Our results demonstrate the engineering of ensembles of elaborate quantum resonance states by molecular self-assembly at surfaces.